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Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs

The present study addresses the numerical solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions across three distinct domains: a unit rectangle with a quarter-circle cutout of radius 0.5, an irregular domain, and a Cassini curve. Dirichlet bo...

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Main Authors: Ahmad M., Khan M.N., Ahmad I.
Other Authors: 56477924900
Format: Article
Published: Springer Science and Business Media Deutschland GmbH 2025
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spelling my.uniten.dspace-369632025-03-03T15:46:09Z Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs Ahmad M. Khan M.N. Ahmad I. 56477924900 57205304990 57220824630 The present study addresses the numerical solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions across three distinct domains: a unit rectangle with a quarter-circle cutout of radius 0.5, an irregular domain, and a Cassini curve. Dirichlet boundary conditions are imposed on specific segments, while nonlocal boundary conditions are applied to the remaining portions. The Kansa method is employed to solve the steady-state heat conduction equation, utilizing three types of radial basis functions (RBFs) to explore the influence of the shape parameter on accuracy and matrix conditioning. These include the inverse multiquadric RBF, a modified inverse multiquadric RBF proposed here for the first time, and a hybrid RBF [1]. As a meshless method, the Kansa approach eliminates the need for mesh generation or node connectivity within local subdomains. To evaluate accuracy and performance, the L� error norm is employed. The results demonstrate the effectiveness of the proposed techniques in solving the 2D steady-state heat conduction problem. A comparative analysis is conducted to assess the accuracy and computational efficiency of the methods. ? The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Article in press 2025-03-03T07:46:09Z 2025-03-03T07:46:09Z 2024 Article 10.1140/epjs/s11734-024-01416-8 2-s2.0-85210527031 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85210527031&doi=10.1140%2fepjs%2fs11734-024-01416-8&partnerID=40&md5=62ce830091074da8791b65c5163e8031 https://irepository.uniten.edu.my/handle/123456789/36963 Springer Science and Business Media Deutschland GmbH Scopus
institution Universiti Tenaga Nasional
building UNITEN Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tenaga Nasional
content_source UNITEN Institutional Repository
url_provider http://dspace.uniten.edu.my/
description The present study addresses the numerical solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions across three distinct domains: a unit rectangle with a quarter-circle cutout of radius 0.5, an irregular domain, and a Cassini curve. Dirichlet boundary conditions are imposed on specific segments, while nonlocal boundary conditions are applied to the remaining portions. The Kansa method is employed to solve the steady-state heat conduction equation, utilizing three types of radial basis functions (RBFs) to explore the influence of the shape parameter on accuracy and matrix conditioning. These include the inverse multiquadric RBF, a modified inverse multiquadric RBF proposed here for the first time, and a hybrid RBF [1]. As a meshless method, the Kansa approach eliminates the need for mesh generation or node connectivity within local subdomains. To evaluate accuracy and performance, the L� error norm is employed. The results demonstrate the effectiveness of the proposed techniques in solving the 2D steady-state heat conduction problem. A comparative analysis is conducted to assess the accuracy and computational efficiency of the methods. ? The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024.
author2 56477924900
author_facet 56477924900
Ahmad M.
Khan M.N.
Ahmad I.
format Article
author Ahmad M.
Khan M.N.
Ahmad I.
spellingShingle Ahmad M.
Khan M.N.
Ahmad I.
Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
author_sort Ahmad M.
title Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
title_short Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
title_full Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
title_fullStr Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
title_full_unstemmed Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs
title_sort local meshless methods for elliptic pdes with multipoint boundary conditions: investigating efficiency and accuracy of various rbfs
publisher Springer Science and Business Media Deutschland GmbH
publishDate 2025
_version_ 1825816037944197120
score 13.244413

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